Under Kim's watch, North Korea has maintained a torrid pace in weapons tests, including its most powerful nuclear test to date on September 3 and two July flight tests of intercontinental ballistic missiles that could strike deep into the USA mainland when perfected.
Hawkish Japanese Prime Minister Shinzo Abe has said he would "never tolerate" the North's "dangerous provocative action" and has urged the global community to ramp up pressure on Pyongyang.
Pyongyang launched a second ballistic missile across Japan two weeks later.
What to do about the North Korean crisis?
In response to new sanctions - imposed after the country's sixth and most powerful nuclear test - the state has said it will now accelerate its nuclear programme.
Mr Trump raised eyebrows on Sunday when he described the North Korean leader as "Rocket Man" in a provocative tweet. A pair of USA bombers and four F-35 jets joined South Korean fighters, Seoul's defense ministry said.
The UN Security Council last week unanimously passed a US-drafted resolution that imposes strongest sanctions ever on North Korea, including restricting its oil imports and banning textile exports, to curb the reclusive nation's nuclear programme.
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Trump has threatened to rain "fire and fury" on North Korea.
Part of the reason why UN sanctions against North Korea have been unsuccessful is that, while the UN has asked other countries to cut their ties with the rogue state, North Korea still receives resources from sympathizing nations.
Days before President Trump's first speech before the U.N. General Assembly, Ms. Haley said that "we've pretty much exhausted all the things we can do at the [U.N.] Security Council at this point".
Still, despite heated rhetoric and posturing in the United States and North Korea, there has been no positioning of us military assets to suggest a military conflict is imminent.
The regime wanted to display its displeasure at the latest round of United Nations sanctions, which were imposed following North Korea's sixth nuclear test on 3 September, its most powerful to date.
"The bottom line is that in the missiles, were they to be a threat, whether it be the United States territory Guam, obviously Japan, Japan's territory, that would elicit a different response from us", he said.